Question

Find the inverse of the linear function y= 1/2x+3

Answer 1

Answer:  The inverse of the given function is $y=2x-6.$

Step-by-step explanation:  We are given to find the inverse of the following linear function :

$y=\dfrac{1}{2}x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)$

The inverse of y = f(x) is written as

$x=f^{-1}(y).$

Substituting the above in equation (i), we get

$y=\dfrac{1}{2}x+3\\\\\Rightarrow y=\dfrac{1}{2}f^{-1}(y)+3\\\\\Rightarrow \dfrac{1}{2}f^{-1}(y)=y-3\\\\\Rightarrow f^{-1}(y)=2(y-3)\\\\\Rightarrow f^{-1}(y)=2y-6.$

Thus, the inverse of the given function is $y=2x-6.$